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• A look at the numbers behind England’s opening partnerships

  England go into an eagerly anticipated summer of Test cricket hoping Ben Duckett and Zak Crawley have finally solved their long-standing problems at the top of the order.

  Duckett’s average of 56.44 is by far the highest of any England opener since Sir Alastair Cook’s retirement nearly five years ago, while his strike rate of 95.49 is arguably of even greater importance in the Brendon McCullum/Ben Stokes era.

  He and Crawley average over 48 as a partnership, albeit in just five matches to date, and here the PA news agency looks at their record in contrast to what has gone before.

  Immediate impact

  Crawley and Duckett’s first innings together set the bar high as they put on 233 against Pakistan in Rawalpindi in December.

  Those runs came in just 35.4 overs at a rate of 6.7 per over as both men scored centuries – as did Ollie Pope and Harry Brook, all at over a run a ball apart from Duckett’s 107 from 110 balls.

  It would be asking a lot for their partnership to live up to those heights since, and Duckett was dismissed first ball in the second innings, but in two of the four Tests since they have a fifty partnership to their name – 87 in Karachi and 52 against New Zealand at Mount Maunganui.

  Even their 38 in Multan and 39 in Wellington would be an improvement on England’s average opening partnership of 28.40 since Cook retired, while their strike rate has settled at a still-impressive 5.70 per over.

  The last five years

  Duckett is the 12th opener used by England in 56 Tests since Cook’s departure, with only five of those even averaging over 30.

  His average is almost 10 runs clear of the field, though second is regular tail-ender Jack Leach whose 46.50 comes from scores of 92 and one in two innings as a nightwatchman. Captain Ben Stokes has no average as an opener, having scored 78 not out from 57 balls in his only innings.

  Keaton Jennings, Joe Denly and Rory Burns average narrowly over 30 while Crawley is at 25.19, which also ranks him behind Dom Sibley. His strike rate of 57.90, while pedestrian by England’s new standard, ranks third in that time and rises to 83.47 in innings partnering Duckett.

  Haseeb Hameed limped to an average of 19.18 and a strike rate of 30.80, Alex Lees was not much better at 23.84 and 43.06, Jason Roy made only 62 runs in seven innings and Jos Buttler was promoted once as a pinch-hitter but failed to score.

  The only other post-Cook pairings to average even 30 are Burns’ partnerships with Hameed (39.14) and Crawley (35.00).

  Long-term trend

  The issue has existed even since the departure of Cook’s predecessor as captain, Sir Andrew Strauss, back in August 2012.

  Cook averaged 42.52 from 144 innings in that time but only three other openers hit the 40 mark.

  Encouragingly, one of those is Duckett with 46.15 for his full 14 innings as an international opener. His strike rate across that whole period sits at 89.55.

  Joe Root spent 11 innings at the top of the order and while his average of 41.70 was more than creditable, it was well down on his overall Test average of 50.22. Leach is the third name on the list, in the two aforementioned innings.

• On This Day in 2015: England captain reaches a significant milestone

  Alastair Cook became England’s all-time leading Test run-scorer on this day in 2015, surpassing his own mentor Graham Gooch.

  England’s then-Test captain set the new benchmark on the second afternoon of the second Test against New Zealand at Headingley when he square-drove Tim Southee for four to reach 33 in his 203rd innings – and 8,902 in aggregate.

  Gooch’s haul of 8,900 had stood for 20 years as England’s historic benchmark, and Cook insisted before the start of this match that he would never consider himself in the class of the man who had taught him much of what he knew, through their close working relationship and friendship since his school days.

  “It is a very special day for me personally,” he said. “I can’t really describe it, to be on top of the list. I don’t deserve to be there with the way I play.

  “You don’t play for the records – but I know I needed 32 runs. But to break the record, you want to do it with an innings (that matters). It was an amazing moment, very humbling.”

  Cook had endured a turbulent previous year-and-a-half, having overseen a 5-0 Ashes defeat, the end of Kevin Pietersen’s international career and lows in form in both Tests and one-day internationals that led to him being stripped as England captain in the latter format two months before the World Cup.

  “The last 18 months have been tough personally as a captain,” Cook said after an innings of 75 against the Black Caps.

  “A lot of stuff has gone on the last four or five months, but I have given time to my game and I feel like it is going well.”

  Cook ended his international career in September 2018, having amassed 12,472 Test runs including 33 centuries – both a record for an England batter.

• Lancashire slip to first defeat of Blast season against Birmingham

  Lancashire suffered their first defeat of this season’s Vitality Blast as they slumped to a seven-wicket loss at Birmingham Bears on Monday.

  The Lightning lost their last seven wickets for 36 runs in 35 balls as they were bowled out for just 98 at Edgbaston.

  Spinners Danny Briggs and Dan Mousley did most of the damage, taking four for 15 and three for 13 respectively.

  The Bears then eased to victory, maintaining their own 100 per cent record in the competition, with captain Alex Davies, formerly of Lancashire, hitting an unbeaten 51 from 39 balls.

  Worcestershire claimed their third win from three outings as they saw off Leicestershire by 33 runs at New Road.

  Kashif Ali top-scored with 69 – his maiden half-century in the Blast – as the Rapids posted 183 for seven from their 20 overs.

  Leicestershire reached 70 for one in reply but then fell away as Brett D’Oliveira, Michael Bracewell and Usama Mir all took two wickets apiece and Pat Brown (three for 25) cut through the tail.

  Northamptonshire claimed their first win as they beat Derbyshire by six wickets with 12 balls to spare at Derby.

  Saif Zaib led them home with 37 not out from 32 balls while captain David Willey and Chris Lynn added 31 as the Steelbacks eased to their 152-run target.

  Wayne Madsen had top-scored for Derbyshire with 57 and wicketkeeper Brooke Guest weighed in with 49.

  Gloucestershire held on for a nail-biting two-run win over Middlesex in a high-scoring contest at Northwood.

  Miles Hammond hit 59 from 42 balls and Grant Roelofsen 34 from 19 as Gloucestershire ran up 181 for nine from their 20 overs.

  Stephen Eskinazi (59) and Joe Cracknell (42) got Middlesex off to a strong start in reply before Luke Hollman (39) and Ryan Higgins (24) took up the chase.

  Seven runs were needed off the final over but Matt Taylor conceded just four with Higgins run out off the last ball.